FIA NLS Models: Biomass vs. Stand Age, G-Reconciled – Data Subsets
JAH
2023-04-25
Background
This analysis document compliments FIA NLS Models: Biomass vs. Stand Age, G-Reconciled. All of the background information from that document applies to these analyses, which are extensions to them. The difference between that document and this analysis is the use of different data subsets.
Here, we fit the models using: 1) a temporally-balanced dataset, where we take the first and most-recent plot record for all plots in the dataset, 2) a temporally-balanced dataset (same as #1), but which excludes plot locations which have experienced harvest (at any point over the study interval 2000-2022)
Below the model fitting procedure is implemented by ecoprovince:
Analysis 1: Temporally-balanced analysis
211 - Northeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4834 1203.6
## 2 4798 1069.7 36 133.94 16.688 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 52557.62
## 2 2 51701.49##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.45296 0.16808 2.695 0.00707 **
## alpha 0.85982 0.03444 24.965 < 2e-16 ***
## A 441.85673 32.45109 13.616 < 2e-16 ***
## k 185.76466 15.60336 11.905 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4722 on 4798 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 6.831e-06
## (36 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in Mod.Sel3 %in% c(1, "1a", "1b", "1c", 4) :
## object 'Mod.Sel3' not found
## Error in Mod.Sel3 %in% c(1, "1a", "1b", "1c", 4) :
## object 'Mod.Sel3' not found
## Error in Mod.Sel3 %in% c(1, "1a", "1b", "1c", 4) :
## object 'Mod.Sel3' not found
## model AIC
## 1 2 51701.49
## 2 2a NA
## 3 2b NA
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.45296 0.16808 2.695 0.00707 **
## alpha 0.85982 0.03444 24.965 < 2e-16 ***
## A 441.85673 32.45109 13.616 < 2e-16 ***
## k 185.76466 15.60336 11.905 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4722 on 4798 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 6.831e-06
## (36 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4832 1179.6
## 2 4796 1035.9 36 143.7 18.481 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 51701.49
## 2 4 52463.90
## 3 5 51551.15##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.65379 0.18036 3.625 0.000292 ***
## alpha 0.85353 0.03265 26.139 < 2e-16 ***
## a 40.11843 1.93712 20.710 < 2e-16 ***
## b 108.90495 5.15248 21.136 < 2e-16 ***
## c 111.29913 4.38564 25.378 < 2e-16 ***
## d 0.89265 0.04335 20.590 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4647 on 4796 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (36 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.98547, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -29.391, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
plotting 2
212 - Laurentian Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12943 5165.4
## 2 9753 3585.0 3190 1580.4 1.3478 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 135621.4
## 2 2 102123.0##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.29724 0.14081 2.111 0.0348 *
## alpha 0.70267 0.03058 22.981 <2e-16 ***
## A 176.59075 6.88136 25.662 <2e-16 ***
## k 65.09491 2.73847 23.771 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6063 on 9753 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 1.083e-06
## (3205 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 9753 3585.0
## 2 9752 3519.8 1 65.171 180.56 < 2.2e-16 ***
## 3 9751 3435.0 1 84.865 240.91 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 102123.0
## 2 2a 101946.0
## 3 2b NA
## 4 2c 101709.9##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 4.146e-01 1.447e-01 2.866 0.00417 **
## alpha 7.877e-01 2.022e-02 38.958 < 2e-16 ***
## A 1.192e+02 5.082e+00 23.445 < 2e-16 ***
## k 4.626e+01 1.588e+00 29.129 < 2e-16 ***
## p 1.983e-01 9.842e-03 20.151 < 2e-16 ***
## s 2.363e+00 1.349e-01 17.510 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5935 on 9751 degrees of freedom
##
## Number of iterations to convergence: 17
## Achieved convergence tolerance: 6.728e-06
## (3205 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12941 5088.9
## 2 9751 3422.9 3190 1666 1.4878 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2c 101709.9
## 2 4 135432.3
## 3 5 101675.5##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.43833 0.14548 3.013 0.00259 **
## alpha 0.79235 0.01979 40.034 < 2e-16 ***
## a 24.18608 0.95524 25.319 < 2e-16 ***
## b 82.87045 3.17194 26.126 < 2e-16 ***
## c 118.37742 5.24621 22.564 < 2e-16 ***
## d 1.24425 0.04485 27.744 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5925 on 9751 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (3205 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
predict and plot
plotting 2
221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5442 948.80
## 2 5405 844.43 37 104.37 18.056 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 59550.63
## 2 2 58624.29##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.18125 0.12626 1.436 0.151
## alpha 0.81310 0.03087 26.342 <2e-16 ***
## A 475.26137 28.14567 16.886 <2e-16 ***
## k 144.59688 10.07385 14.354 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3953 on 5405 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 8.453e-06
## (37 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5405 844.43
## 2 5404 844.31 1 0.11852 0.7586 0.3838
## model AIC
## 1 2 58624.29
## 2 2a 58625.53
## 3 2b 58611.28
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.22671 0.12920 1.755 0.0794 .
## alpha 0.81954 0.03110 26.352 < 2e-16 ***
## A 317.53226 27.47471 11.557 < 2e-16 ***
## k 72.74922 9.29982 7.823 6.18e-15 ***
## s 1.22840 0.06082 20.198 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3947 on 5404 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 2.529e-06
## (37 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5440 940.37
## 2 5403 834.50 37 105.87 18.526 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2b 58611.28
## 2 4 59506.03
## 3 5 58564.32##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.23356 0.12884 1.813 0.0699 .
## alpha 0.81405 0.02994 27.189 <2e-16 ***
## a 29.92583 2.74687 10.895 <2e-16 ***
## b 166.53295 9.14543 18.209 <2e-16 ***
## c 142.75974 12.21268 11.689 <2e-16 ***
## d 1.37522 0.08076 17.028 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.393 on 5403 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (37 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
predict and plot
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
plotting 2
222 - Midwest Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3547 1178.60
## 2 2737 841.95 810 336.65 1.3511 2.251e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## model AIC
## 1 1 38157.03
## 2 2 29481.92##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.05380 0.22291 -0.241 0.809
## alpha 0.82138 0.05547 14.807 < 2e-16 ***
## A 490.38839 58.25668 8.418 < 2e-16 ***
## k 204.96549 26.97852 7.597 4.12e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5546 on 2737 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 7.026e-06
## (811 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2737 841.95
## 2 2736 841.65 1 0.29896 0.9718 0.3243
## model AIC
## 1 2 29481.92
## 2 2a 29482.95
## 3 2b NA
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.05380 0.22291 -0.241 0.809
## alpha 0.82138 0.05547 14.807 < 2e-16 ***
## A 490.38839 58.25668 8.418 < 2e-16 ***
## k 204.96549 26.97852 7.597 4.12e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5546 on 2737 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 7.026e-06
## (811 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3545 1160.08
## 2 2735 816.94 810 343.14 1.4183 9.125e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 29481.92
## 2 4 38104.80
## 3 5 29403.25##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.10510 0.23599 0.445 0.656
## alpha 0.84430 0.04755 17.755 <2e-16 ***
## a 26.79295 2.19579 12.202 <2e-16 ***
## b 119.86978 7.84054 15.288 <2e-16 ***
## c 104.72053 6.16485 16.987 <2e-16 ***
## d 1.01830 0.06210 16.399 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5465 on 2735 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (811 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.95843, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -17.144, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
223 - Central Interior Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6383 1208.6
## 2 5254 961.6 1129 247.02 1.1954 4.219e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 66739.63
## 2 2 54968.25##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.24143 0.10087 -2.394 0.0167 *
## alpha 0.75149 0.03396 22.126 <2e-16 ***
## A 280.04402 12.75403 21.957 <2e-16 ***
## k 75.92965 4.71986 16.087 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4278 on 5254 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 2.163e-06
## (1130 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5254 961.60
## 2 5253 961.55 1 0.050724 0.2771 0.5986
## model AIC
## 1 2 54968.25
## 2 2a 54969.97
## 3 2b 54944.08
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.21532 0.10199 -2.111 0.0348 *
## alpha 0.76003 0.03415 22.252 <2e-16 ***
## A 197.02836 11.07963 17.783 <2e-16 ***
## k 40.20400 3.15940 12.725 <2e-16 ***
## s 1.39168 0.07829 17.776 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4268 on 5253 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 4.49e-06
## (1130 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6381 1195.86
## 2 5252 944.25 1129 251.61 1.2396 1.039e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2b 54944.08
## 2 4 66675.81
## 3 5 54876.47##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.19990 0.10190 -1.962 0.0499 *
## alpha 0.76139 0.03295 23.109 <2e-16 ***
## a 31.44052 2.90774 10.813 <2e-16 ***
## b 117.40892 5.13663 22.857 <2e-16 ***
## c 106.43481 6.07269 17.527 <2e-16 ***
## d 1.26371 0.07423 17.025 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.424 on 5252 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1130 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
predict and plot
plotting 2
231 - Southeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7773 2698.5
## 2 7641 2403.0 132 295.47 7.1178 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 85845.56
## 2 2 84004.19##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.24455 0.16444 7.568 4.22e-14 ***
## alpha 0.61526 0.02415 25.474 < 2e-16 ***
## A 225.38333 8.98763 25.077 < 2e-16 ***
## k 51.58983 2.13778 24.132 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5608 on 7641 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 2.792e-06
## (145 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_231, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7641 2403.0
## 2 7640 2305.6 1 97.387 322.71 < 2.2e-16 ***
## 3 7639 2248.7 1 56.920 193.36 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 84004.19
## 2 2a 83689.90
## 3 2b NA
## 4 2c 83500.79##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.94524 0.20024 9.714 <2e-16 ***
## alpha 0.78032 0.01528 51.081 <2e-16 ***
## A 133.15240 5.75310 23.144 <2e-16 ***
## k 32.45965 1.18392 27.417 <2e-16 ***
## p 0.18680 0.00947 19.725 <2e-16 ***
## s 2.28738 0.12712 17.993 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5426 on 7639 degrees of freedom
##
## Number of iterations to convergence: 15
## Achieved convergence tolerance: 7.759e-06
## (145 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7771 2669.8
## 2 7639 2247.0 132 422.83 10.89 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2c 83500.79
## 2 4 85766.57
## 3 5 83495.02##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.90303 0.19764 9.629 <2e-16 ***
## alpha 0.78032 0.01523 51.226 <2e-16 ***
## a 25.28966 0.92631 27.302 <2e-16 ***
## b 102.66192 4.92792 20.833 <2e-16 ***
## c 105.45753 7.79762 13.524 <2e-16 ***
## d 1.43411 0.06273 22.863 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5424 on 7639 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (145 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
predict and plot
plotting 2
232 - Outer Coastal Plain Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7905 4072.2
## 2 7735 3735.2 170 337 4.1052 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 88878.43
## 2 2 86870.95##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.87141 0.18185 4.792 1.68e-06 ***
## alpha 0.61236 0.02685 22.805 < 2e-16 ***
## A 226.00187 10.95493 20.630 < 2e-16 ***
## k 52.18677 2.65052 19.689 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6949 on 7735 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 9.209e-06
## (201 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_232, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7735 3735.2
## 2 7734 3566.1 1 169.117 366.77 < 2.2e-16 ***
## 3 7733 3492.2 1 73.924 163.70 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 86870.95
## 2 2a 86514.38
## 3 2b NA
## 4 2c 86354.27##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.42439 0.20918 6.809 1.05e-11 ***
## alpha 0.81600 0.01492 54.697 < 2e-16 ***
## A 138.37803 6.92119 19.993 < 2e-16 ***
## k 34.69364 1.48237 23.404 < 2e-16 ***
## p 0.20268 0.01124 18.025 < 2e-16 ***
## s 2.36450 0.15700 15.061 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.672 on 7733 degrees of freedom
##
## Number of iterations to convergence: 28
## Achieved convergence tolerance: 7.627e-06
## (201 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7903 4029.5
## 2 7733 3489.9 170 539.64 7.0338 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2c 86354.27
## 2 4 88799.14
## 3 5 86349.26##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.38952 0.20683 6.718 1.97e-11 ***
## alpha 0.81558 0.01491 54.719 < 2e-16 ***
## a 28.36270 1.17948 24.047 < 2e-16 ***
## b 107.28397 6.15566 17.429 < 2e-16 ***
## c 114.33118 10.35916 11.037 < 2e-16 ***
## d 1.42115 0.07470 19.026 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6718 on 7733 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (201 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
predict and plot
plotting 2
234 - Lower Mississippi Riverine Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 826 218.04
## 2 797 177.06 29 40.981 6.3612 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 9094.121
## 2 2 8721.045##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.38005 0.41044 0.926 0.354753
## alpha 0.79101 0.06552 12.072 < 2e-16 ***
## A 727.26287 186.87440 3.892 0.000108 ***
## k 253.92949 73.93286 3.435 0.000624 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4713 on 797 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 7.387e-06
## (29 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 797 177.06
## 2 796 176.99 1 0.066994 0.3013 0.5832
## model AIC
## 1 2 8721.045
## 2 2a 8722.742
## 3 2b 8722.583
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.38005 0.41044 0.926 0.354753
## alpha 0.79101 0.06552 12.072 < 2e-16 ***
## A 727.26287 186.87440 3.892 0.000108 ***
## k 253.92949 73.93286 3.435 0.000624 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4713 on 797 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 7.387e-06
## (29 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 824 216.69
## 2 795 176.77 29 39.917 6.1905 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 8721.045
## 2 4 9092.966
## 3 5 8723.743##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.38005 0.41044 0.926 0.354753
## alpha 0.79101 0.06552 12.072 < 2e-16 ***
## A 727.26287 186.87440 3.892 0.000108 ***
## k 253.92949 73.93286 3.435 0.000624 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4713 on 797 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 7.387e-06
## (29 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.95645, p-value = 1.14e-14
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -9.7724, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
242 - Pacific Lowland Mixed Forest
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"251 - Prairie Parkland (Temperate)
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1387 347.56
## 2 977 201.46 410 146.1 1.7282 5.294e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 14526.30
## 2 2 10147.91##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.55006 0.39958 1.377 0.169
## alpha 0.73603 0.08646 8.513 < 2e-16 ***
## A 237.88617 31.29383 7.602 6.84e-14 ***
## k 97.25401 14.53331 6.692 3.71e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4541 on 977 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 4.859e-06
## (411 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 977 201.46
## 2 976 199.66 1 1.7989 8.7938 0.003096 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 10147.91
## 2 2a 10141.11
## 3 2b 10131.28
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.53042 0.39173 1.354 0.176
## alpha 0.75343 0.08629 8.731 < 2e-16 ***
## A 133.20058 14.88028 8.951 < 2e-16 ***
## k 36.74746 3.31677 11.079 < 2e-16 ***
## s 1.91517 0.23582 8.121 1.38e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.45 on 976 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 9.775e-06
## (411 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1385 337.23
## 2 975 196.75 410 140.48 1.6979 2.506e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2b 10131.28
## 2 4 14488.37
## 3 5 10128.73##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.52834 0.39012 1.354 0.17595
## alpha 0.75256 0.08617 8.734 < 2e-16 ***
## a 20.68236 7.88059 2.624 0.00881 **
## b 94.56738 11.99423 7.884 8.43e-15 ***
## c 104.72317 10.86129 9.642 < 2e-16 ***
## d 1.19567 0.16607 7.200 1.20e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4492 on 975 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (411 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.97093, p-value = 4.2e-13
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -7.8881, p-value = 3.068e-15
## alternative hypothesis: two.sidedpredict and plot
plotting 2
255 - Prairie Parkland (Subtropical)
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 439 237.09
## 2 415 203.74 24 33.357 2.8311 1.41e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 4609.958
## 2 2 4397.209##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.1056 0.5547 -0.190 0.84905
## alpha 0.5121 0.1326 3.862 0.00013 ***
## A 168.6419 32.7168 5.155 3.94e-07 ***
## k 48.6765 11.1115 4.381 1.50e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7007 on 415 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 3.1e-06
## (25 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_255, :
## number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 415 203.74
## 2 414 195.16 1 8.5821 18.206 2.459e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 4397.209
## 2 2a 4381.176
## 3 2b NA
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.15195 0.60637 0.251 0.802
## alpha 0.64504 0.09663 6.675 7.94e-11 ***
## A 351.27751 253.84534 1.384 0.167
## k 210.90305 205.28194 1.027 0.305
## p 0.04288 0.02451 1.749 0.081 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6866 on 414 degrees of freedom
##
## Number of iterations to convergence: 17
## Achieved convergence tolerance: 9.28e-06
## (25 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 437 226.64
## 2 413 182.67 24 43.97 4.1422 8.462e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 4381.176
## 2 4 4594.028
## 3 5 4355.477##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.12210 0.57592 0.212 0.832
## alpha 0.72207 0.08129 8.883 < 2e-16 ***
## a 24.95845 3.47359 7.185 3.16e-12 ***
## b 67.55158 9.95661 6.785 4.05e-11 ***
## c 54.80784 4.96595 11.037 < 2e-16 ***
## d 0.85562 0.11721 7.300 1.49e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6651 on 413 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (25 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94116, p-value = 7.913e-12
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -5.1247, p-value = 2.98e-07
## alternative hypothesis: two.sidedpredict and plot
plotting 2
261 - California Coastal Chaparral Forest and Shrub
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
add p model: does not fit
add s model: does not fit
add s+p model: does not fit
unable to fit model (only 64 observations)
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"262 - California Dry Steppe
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
add p model: does not fit
add s model: does not fit
add s+p model: does not fit
unable to fit model (0 observations)
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"263 - California Coastal Steppe - Mixed Forest and Redwood Forest
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"313 - Colorado Plateau Semi-Desert
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"315 - Southwest Plateau and Plains Dry Steppe and Shrub
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"321 - Chihuahuan Semi-Desert
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"322 - American Semidesert and Desert
model selection 1
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed## model AIC
## 1 1 NA
## 2 2 NA## Warning in min(AIC1_322$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in get(paste("nls_322.", Mod.Sel1, sep = "")) :
## object 'nls_322.' not foundsummary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"- Cannot fit model
- not enough data (only 3 observations)
331 - Great Plains/Palouse Dry Steppe
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"- Cannot fit model
332 - Great Plains Steppe
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 149 87.775
## 2 135 78.204 14 9.5719 1.1803 0.2973
## model AIC
## 1 1 1640.707
## 2 2 1511.918##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 2.1120 3.1747 0.665 0.507015
## alpha 1.0245 0.2893 3.541 0.000547 ***
## A 156.2869 107.8495 1.449 0.149623
## k 98.9969 67.6450 1.463 0.145662
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7611 on 135 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.794e-06
## (15 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_332, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_332, :
## number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 2 1511.918
## 2 2a NA
## 3 2b NA
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 2.1120 3.1747 0.665 0.507015
## alpha 1.0245 0.2893 3.541 0.000547 ***
## A 156.2869 107.8495 1.449 0.149623
## k 98.9969 67.6450 1.463 0.145662
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7611 on 135 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.794e-06
## (15 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 147 83.369
## 2 133 72.689 14 10.681 1.3959 0.1634
## model AIC
## 1 2 1511.918
## 2 4 1636.879
## 3 5 1505.753##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 2.4537 3.4077 0.720 0.472762
## alpha 1.0341 0.2776 3.726 0.000287 ***
## a 23.3168 14.0511 1.659 0.099387 .
## b 50.1805 35.1768 1.427 0.156061
## c 117.3875 96.4037 1.218 0.225507
## d 1.0737 0.7345 1.462 0.146177
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7393 on 133 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (15 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.87838, p-value = 2.671e-09
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -3.8886, p-value = 0.0001008
## alternative hypothesis: two.sidedpredict and plot
plotting 2
341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"- model not fitted because only 62 observations
predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"342 - Intermountain Semi-Desert
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"411 - Everglades
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5103 963.25
## 2 5088 823.59 15 139.66 57.52 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 54262.24
## 2 2 53363.88##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.61018 0.16014 3.81 0.00014 ***
## alpha 0.80897 0.02637 30.68 < 2e-16 ***
## A 426.11432 26.45628 16.11 < 2e-16 ***
## k 183.74661 12.18665 15.08 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4023 on 5088 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 2.251e-06
## (16 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5088 823.59
## 2 5087 818.90 1 4.6942 29.16 6.965e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 53363.88
## 2 2a 53336.78
## 3 2b 53318.03
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.50399 0.15320 3.29 0.00101 **
## alpha 0.81807 0.02655 30.81 < 2e-16 ***
## A 241.28488 15.98660 15.09 < 2e-16 ***
## k 67.75381 6.25656 10.83 < 2e-16 ***
## s 1.34274 0.05479 24.51 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4005 on 5087 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 5.361e-06
## (16 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5101 952.58
## 2 5086 812.95 15 139.64 58.24 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2b 53318.03
## 2 4 54209.36
## 3 5 53301.62##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.54177 0.15584 3.476 0.000512 ***
## alpha 0.82011 0.02606 31.468 < 2e-16 ***
## a 19.48450 2.77004 7.034 2.27e-12 ***
## b 148.35643 9.29773 15.956 < 2e-16 ***
## c 170.73931 17.15590 9.952 < 2e-16 ***
## d 1.50104 0.09603 15.631 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3998 on 5086 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (16 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
predict and plot
plotting 2
M221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5180 879.40
## 2 5152 813.08 28 66.326 15.01 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 57351.18
## 2 2 56719.09##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.68286 0.13121 5.204 2.02e-07 ***
## alpha 0.83316 0.04158 20.037 < 2e-16 ***
## A 260.95757 9.61560 27.139 < 2e-16 ***
## k 58.45777 2.94821 19.828 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3973 on 5152 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.421e-06
## (30 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5152 813.08
## 2 5151 813.08 1 0.001 0.0064 0.9364
## 3 5151 808.98 0 0.000
## 4 5150 789.87 1 19.115 124.6319 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 56719.09
## 2 2a 56721.09
## 3 2b 56695.08
## 4 2c 56573.79##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.85782 0.13912 6.166 7.54e-10 ***
## alpha 0.83626 0.03790 22.064 < 2e-16 ***
## A 160.54030 5.31529 30.203 < 2e-16 ***
## k 38.73561 1.03371 37.472 < 2e-16 ***
## p 0.25893 0.01761 14.700 < 2e-16 ***
## s 3.00269 0.23160 12.965 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3916 on 5150 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 5.888e-06
## (30 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5178 862.65
## 2 5150 789.00 28 73.645 17.168 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2c 56573.79
## 2 4 57255.49
## 3 5 56568.14##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.84622 0.13822 6.122 9.92e-10 ***
## alpha 0.83474 0.03806 21.933 < 2e-16 ***
## a 40.58261 2.60780 15.562 < 2e-16 ***
## b 114.46846 4.25585 26.897 < 2e-16 ***
## c 100.35558 3.56301 28.166 < 2e-16 ***
## d 1.16211 0.05532 21.009 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3914 on 5150 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (30 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
predict and plot
plotting 2
M223 - Ozark Broadleaf Forest Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 596 80.866
## 2 594 71.782 2 9.0843 37.587 4.262e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 6115.535
## 2 2 6038.933##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.08126 0.26259 -0.309 0.757
## alpha 0.90022 0.09742 9.240 < 2e-16 ***
## A 296.62823 41.14427 7.209 1.72e-12 ***
## k 94.57333 18.56239 5.095 4.69e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3476 on 594 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 6.315e-06
## (4 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M223, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 594 71.782
## 2 593 71.691 1 0.091014 0.7528 0.3859
## model AIC
## 1 2 6038.933
## 2 2a 6040.174
## 3 2b 6040.650
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.08126 0.26259 -0.309 0.757
## alpha 0.90022 0.09742 9.240 < 2e-16 ***
## A 296.62823 41.14427 7.209 1.72e-12 ***
## k 94.57333 18.56239 5.095 4.69e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3476 on 594 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 6.315e-06
## (4 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 594 80.723
## 2 592 71.703 2 9.0193 37.233 5.875e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 6038.933
## 2 4 6118.473
## 3 5 6042.280##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.08126 0.26259 -0.309 0.757
## alpha 0.90022 0.09742 9.240 < 2e-16 ***
## A 296.62823 41.14427 7.209 1.72e-12 ***
## k 94.57333 18.56239 5.095 4.69e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3476 on 594 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 6.315e-06
## (4 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96672, p-value = 2.129e-10
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -8.7629, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M231 - Ouachita Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 676 152.77
## 2 669 137.62 7 15.149 10.521 1.394e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 7025.553
## 2 2 6913.733##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.6315 0.5100 1.238 0.216
## alpha 0.8739 0.1113 7.855 1.60e-14 ***
## A 286.5998 53.3736 5.370 1.09e-07 ***
## k 130.2058 27.4446 4.744 2.56e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4536 on 669 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 1.757e-06
## (7 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 669 137.62
## 2 668 137.27 1 0.35126 1.7094 0.1915
## model AIC
## 1 2 6913.733
## 2 2a 6914.013
## 3 2b 6914.673
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.6315 0.5100 1.238 0.216
## alpha 0.8739 0.1113 7.855 1.60e-14 ***
## A 286.5998 53.3736 5.370 1.09e-07 ***
## k 130.2058 27.4446 4.744 2.56e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4536 on 669 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 1.757e-06
## (7 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 674 152.71
## 2 667 136.87 7 15.836 11.024 3.181e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 6913.733
## 2 4 7029.273
## 3 5 6914.058##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.6315 0.5100 1.238 0.216
## alpha 0.8739 0.1113 7.855 1.60e-14 ***
## A 286.5998 53.3736 5.370 1.09e-07 ***
## k 130.2058 27.4446 4.744 2.56e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4536 on 669 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 1.757e-06
## (7 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96065, p-value = 1.886e-12
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -8.6968, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M242 - Cascade Mixed Forest
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 326 100.337
## 2 159 52.836 167 47.502 0.856 0.8395
## model AIC
## 1 1 3504.259
## 2 2 1757.521##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.4911 1.4021 -1.064 0.28917
## alpha 0.7692 0.2686 2.864 0.00475 **
## A 199.4827 135.7096 1.470 0.14356
## k 14.6863 10.3710 1.416 0.15870
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5765 on 159 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 5.404e-06
## (167 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 159 52.836
## 2 158 52.385 1 0.45081 1.3597 0.2453
## model AIC
## 1 2 1757.521
## 2 2a 1758.125
## 3 2b NA
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.4911 1.4021 -1.064 0.28917
## alpha 0.7692 0.2686 2.864 0.00475 **
## A 199.4827 135.7096 1.470 0.14356
## k 14.6863 10.3710 1.416 0.15870
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5765 on 159 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 5.404e-06
## (167 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 324 96.856
## 2 157 50.310 167 46.546 0.8698 0.8127
## model AIC
## 1 2 1757.521
## 2 4 3496.641
## 3 5 1753.538##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.5154 1.3312 -1.138 0.2567
## alpha 0.6590 0.2942 2.240 0.0265 *
## a 0.0000 141.2170 0.000 1.0000
## b 188.9583 180.2107 1.049 0.2960
## c 113.2014 16.3494 6.924 1.06e-10 ***
## d 1.7043 0.9728 1.752 0.0817 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5661 on 157 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (167 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.98242, p-value = 0.03655
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = 0.2756, p-value = 0.7829
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M262 - California coastal range - coniferous forest - open woodland - shrub meadow
Model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"- model can fit - but K is negative (only 19 observations) - model excluded
predict and plot
## [1] "cannot plot data with prediction"plotting 2
M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M334 - Black Hills Coniferous Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 299 124.348
## 2 213 86.589 86 37.759 1.08 0.3252
## model AIC
## 1 1 3013.807
## 2 2 2166.492##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.5945 0.8052 -0.738 0.461088
## alpha 0.7886 0.1334 5.913 1.32e-08 ***
## A 117.3902 32.3159 3.633 0.000352 ***
## k 50.8451 22.4857 2.261 0.024756 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6376 on 213 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 9.886e-06
## (89 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 213 86.589
## 2 212 86.587 1 0.002415 0.0059 0.9388
## 3 212 86.462 0 0.000000
## 4 211 86.173 1 0.288651 0.7068 0.4015
## model AIC
## 1 2 2166.492
## 2 2a 2168.486
## 3 2b 2168.172
## 4 2c 2169.446## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df_bal$Code == "M334", , :
## provided 33 variables to replace 32 variables##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.5945 0.8052 -0.738 0.461088
## alpha 0.7886 0.1334 5.913 1.32e-08 ***
## A 117.3902 32.3159 3.633 0.000352 ***
## k 50.8451 22.4857 2.261 0.024756 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6376 on 213 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 9.886e-06
## (89 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 297 124.069
## 2 211 86.545 86 37.523 1.0638 0.3565
## model AIC
## 1 2 2166.492
## 2 4 3017.126
## 3 5 2170.381##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.5945 0.8052 -0.738 0.461088
## alpha 0.7886 0.1334 5.913 1.32e-08 ***
## A 117.3902 32.3159 3.633 0.000352 ***
## k 50.8451 22.4857 2.261 0.024756 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6376 on 213 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 9.886e-06
## (89 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.92294, p-value = 3.195e-09
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -2.5717, p-value = 0.01012
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
Fitted parameters
Best / selected models by ecoprovince
| Code | Ecoregion | Sel.Mod.2 | Sel.Mod.3 | Best.Mod |
|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | 2 | 5 | 5 |
| 212 | Laurentian Mixed Forest | 2c | 5 | 5 |
| 221 | Eastern Broadleaf Forest | 2b | 5 | 5 |
| 222 | Midwest Broadleaf Forest | 2 | 5 | 5 |
| 223 | Central Interior Broadleaf Forest | 2b | 5 | 5 |
| 231 | Southeastern Mixed Forest | 2c | 5 | 5 |
| 232 | Outer Coastal Plain Mixed Forest | 2c | 5 | 5 |
| 234 | Lower Mississippi Riverine Forest | 2 | 2 | 2 |
| 242 | Pacific Lowland Mixed Forest | NA | NA | NA |
| 251 | Prairie Parkland (Temperate) | 2b | 5 | 5 |
| 255 | Prairie Parkland (Subtropical) | 2a | 5 | 5 |
| 261 | California Coastal Chaparral Forest and Shrub | NA | NA | NA |
| 262 | California Dry Steppe | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | NA | NA | NA |
| 313 | Colorado Plateau Semi-Desert | NA | NA | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | NA | NA | NA |
| 322 | American Semidesert and Desert | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | NA | NA | NA |
| 332 | Great Plains Steppe | 2 | 5 | 5 |
| 341 | Intermountain Semi-Desert and Desert | NA | NA | NA |
| 342 | Intermountain Semi-Desert | NA | NA | NA |
| 411 | Everglades | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | 2b | 5 | 5 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | 2c | 5 | 5 |
| M223 | Ozark Broadleaf Forest Meadow | 2 | 2 | 2 |
| M231 | Ouachita Mixed Forest | 2 | 2 | 2 |
| M242 | Cascade Mixed Forest | NA | NA | NA |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | 2 | 5 | 5 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | NA | NA | NA |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | NA | NA | NA |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | NA | NA | NA |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | NA | NA | NA |
| M334 | Black Hills Coniferous Forest | 2 | 2 | 2 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | NA | NA | NA |
table by ecoprovince
| Code | Ecoregion | region | n.obs | n.plots | tau | tau.variance | tau.2.5 | tau.97.5 | alpha | alpha.variance | alpha.2.5 | alpha.97.5 | A | A.2.5 | A.97.5 | k | k.2.5 | k.97.5 | a | a.2.5 | a.97.5 | b | b.se | b.2.5 | b.97.5 | c | c.2.5 | c.97.5 | d | d.2.5 | d.97.5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | east | 4838 | 2419 | 0.6537893 | 0.0325313 | 0.3001925 | 1.0073861 | 0.8535320 | 0.0010662 | 0.7895172 | 0.9175468 | 441.8567 | 378.23771 | 505.4757 | 185.76466 | 155.174910 | 216.35440 | 40.11843 | 36.320789 | 43.91608 | 108.90495 | NA | 98.80371 | 119.00618 | 111.29913 | 102.70126 | 119.89700 | 0.8926520 | 0.8076609 | 0.9776431 |
| 212 | Laurentian Mixed Forest | east | 12962 | 6481 | 0.4383266 | 0.0211649 | 0.1531525 | 0.7235006 | 0.7923513 | 0.0003917 | 0.7535546 | 0.8311479 | 119.1542 | 109.19192 | 129.1164 | 46.26337 | 43.150146 | 49.37658 | 24.18608 | 22.313610 | 26.05854 | 82.87045 | NA | 76.65278 | 89.08812 | 118.37742 | 108.09375 | 128.66108 | 1.2442510 | 1.1563415 | 1.3321605 |
| 221 | Eastern Broadleaf Forest | east | 5446 | 2723 | 0.2335591 | 0.0166007 | -0.0190263 | 0.4861445 | 0.8140497 | 0.0008964 | 0.7553542 | 0.8727451 | 317.5323 | 263.67075 | 371.3938 | 72.74922 | 54.517828 | 90.98061 | 29.92583 | 24.540863 | 35.31080 | 166.53295 | NA | 148.60422 | 184.46167 | 142.75974 | 118.81797 | 166.70151 | 1.3752196 | 1.2168890 | 1.5335502 |
| 222 | Midwest Broadleaf Forest | east | 3552 | 1776 | 0.1050960 | 0.0556931 | -0.3576483 | 0.5678403 | 0.8442958 | 0.0022613 | 0.7510516 | 0.9375400 | 490.3884 | 376.15688 | 604.6199 | 204.96549 | 152.065171 | 257.86581 | 26.79295 | 22.487375 | 31.09852 | 119.86978 | NA | 104.49581 | 135.24375 | 104.72053 | 92.63230 | 116.80876 | 1.0183031 | 0.8965441 | 1.1400621 |
| 223 | Central Interior Broadleaf Forest | east | 6388 | 3194 | -0.1998960 | 0.0103846 | -0.3996715 | -0.0001205 | 0.7613860 | 0.0010855 | 0.6967954 | 0.8259766 | 197.0284 | 175.30767 | 218.7490 | 40.20400 | 34.010267 | 46.39773 | 31.44052 | 25.740151 | 37.14089 | 117.40892 | NA | 107.33898 | 127.47885 | 106.43481 | 94.52981 | 118.33982 | 1.2637077 | 1.1181891 | 1.4092263 |
| 231 | Southeastern Mixed Forest | east | 7790 | 3895 | 1.9030292 | 0.0390616 | 1.5156002 | 2.2904583 | 0.7803161 | 0.0002320 | 0.7504558 | 0.8101765 | 133.1524 | 121.87475 | 144.4300 | 32.45965 | 30.138849 | 34.78046 | 25.28966 | 23.473843 | 27.10548 | 102.66192 | NA | 93.00185 | 112.32199 | 105.45753 | 90.17205 | 120.74300 | 1.4341111 | 1.3111510 | 1.5570712 |
| 232 | Outer Coastal Plain Mixed Forest | east | 7940 | 3970 | 1.3895246 | 0.0427791 | 0.9840796 | 1.7949695 | 0.8155816 | 0.0002222 | 0.7863637 | 0.8447994 | 138.3780 | 124.81063 | 151.9454 | 34.69364 | 31.787789 | 37.59950 | 28.36270 | 26.050590 | 30.67481 | 107.28397 | NA | 95.21721 | 119.35073 | 114.33118 | 94.02442 | 134.63794 | 1.4211487 | 1.2747245 | 1.5675729 |
| 234 | Lower Mississippi Riverine Forest | east | 830 | 415 | 0.3800485 | 0.1684627 | -0.4256268 | 1.1857237 | 0.7910134 | 0.0042932 | 0.6623967 | 0.9196302 | 727.2629 | 360.43872 | 1094.0870 | 253.92949 | 108.803351 | 399.05563 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 242 | Pacific Lowland Mixed Forest | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 251 | Prairie Parkland (Temperate) | east | 1392 | 696 | 0.5283410 | 0.1521922 | -0.2372270 | 1.2939089 | 0.7525582 | 0.0074250 | 0.5834615 | 0.9216549 | 133.2006 | 103.99955 | 162.4016 | 36.74746 | 30.238646 | 43.25628 | 20.68236 | 5.217490 | 36.14724 | 94.56738 | NA | 71.02990 | 118.10487 | 104.72317 | 83.40898 | 126.03736 | 1.1956671 | 0.8697794 | 1.5215548 |
| 255 | Prairie Parkland (Subtropical) | east | 444 | 222 | 0.1220981 | 0.3316784 | -1.0099927 | 1.2541890 | 0.7220663 | 0.0066076 | 0.5622786 | 0.8818540 | 351.2775 | -147.70896 | 850.2640 | 210.90305 | -192.621828 | 614.42793 | 24.95845 | 18.130329 | 31.78658 | 67.55158 | NA | 47.97963 | 87.12353 | 54.80784 | 45.04615 | 64.56953 | 0.8556187 | 0.6252087 | 1.0860287 |
| 261 | California Coastal Chaparral Forest and Shrub | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 262 | California Dry Steppe | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | pacific | 4 | 2 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 313 | Colorado Plateau Semi-Desert | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 322 | American Semidesert and Desert | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | interior west | 118 | 59 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 332 | Great Plains Steppe | interior west | 154 | 77 | 2.4536877 | 11.6123801 | -4.2865995 | 9.1939750 | 1.0341031 | 0.0770453 | 0.4850798 | 1.5831264 | 156.2869 | -57.00625 | 369.5801 | 98.99687 | -34.784176 | 232.77792 | 23.31681 | -4.475821 | 51.10943 | 50.18053 | NA | -19.39784 | 119.75890 | 117.38752 | -73.29536 | 308.07039 | 1.0736506 | -0.3791879 | 2.5264891 |
| 341 | Intermountain Semi-Desert and Desert | interior west | 4 | 2 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 342 | Intermountain Semi-Desert | interior west | 2 | 1 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 411 | Everglades | east | 66 | 33 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | east | 5108 | 2554 | 0.5417730 | 0.0242861 | 0.2362595 | 0.8472865 | 0.8201066 | 0.0006792 | 0.7690154 | 0.8711978 | 241.2849 | 209.94426 | 272.6255 | 67.75381 | 55.488265 | 80.01935 | 19.48450 | 14.054022 | 24.91497 | 148.35643 | NA | 130.12888 | 166.58398 | 170.73931 | 137.10636 | 204.37226 | 1.5010388 | 1.3127853 | 1.6892923 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | east | 5186 | 2593 | 0.8462159 | 0.0191060 | 0.5752376 | 1.1171943 | 0.8347375 | 0.0014485 | 0.7601251 | 0.9093499 | 160.5403 | 150.12007 | 170.9605 | 38.73561 | 36.709097 | 40.76212 | 40.58261 | 35.470220 | 45.69500 | 114.46846 | NA | 106.12519 | 122.81174 | 100.35558 | 93.37058 | 107.34059 | 1.1621055 | 1.0536627 | 1.2705482 |
| M223 | Ozark Broadleaf Forest Meadow | east | 602 | 301 | -0.0812639 | 0.0689520 | -0.5969759 | 0.4344482 | 0.9002204 | 0.0094914 | 0.7088835 | 1.0915572 | 296.6282 | 215.82228 | 377.4342 | 94.57333 | 58.117443 | 131.02922 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M231 | Ouachita Mixed Forest | east | 680 | 340 | 0.6315443 | 0.2600526 | -0.3697578 | 1.6328464 | 0.8739198 | 0.0123794 | 0.6554535 | 1.0923861 | 286.5998 | 181.79982 | 391.3997 | 130.20582 | 76.317969 | 184.09368 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M242 | Cascade Mixed Forest | pacific | 34 | 17 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | pacific | 330 | 165 | -1.5153914 | 1.7720212 | -4.1447096 | 1.1139269 | 0.6589855 | 0.0865469 | 0.0779075 | 1.2400635 | 199.4827 | -68.54334 | 467.5088 | 14.68629 | -5.796325 | 35.16890 | 0.00000 | -278.930355 | 278.93036 | 188.95825 | NA | -166.99203 | 544.90854 | 113.20139 | 80.90831 | 145.49447 | 1.7042560 | -0.2172067 | 3.6257187 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | interior west | 8 | 4 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 20 | 10 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 22 | 11 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M334 | Black Hills Coniferous Forest | interior west | 306 | 153 | -0.5945383 | 0.6483121 | -2.1816767 | 0.9926002 | 0.7885811 | 0.0177862 | 0.5256970 | 1.0514651 | 117.3902 | 53.69020 | 181.0901 | 50.84512 | 6.522162 | 95.16807 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
plot tau
map
## OGR data source with driver: ESRI Shapefile
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings: PROVINCE_ PROVINCE_I
plot alpha (biomass compensation effect)
plot A (asymptote of B)
## Warning: Removed 19 rows containing missing values (`geom_point()`).
plot k (stand age at half biomass asymptote)
## Warning: Removed 19 rows containing missing values (`geom_point()`).
Caclulations - weighted averages
tau (productivity trend in % 2000-2021)
## region weighted.tau weighted.tau.std_Error 95 % CI, upper
## 1 entire US 0.675858940 0.056786257 0.787160003
## 2 pacific -0.007786242 0.006839707 0.005619585
## 3 east 0.680594405 0.055645458 0.789659503
## 4 interior west 0.003050777 0.009026644 0.020743000
## 95 % CI, lower
## 1 0.56455788
## 2 -0.02119207
## 3 0.57152931
## 4 -0.01464145alpha (biomass compensation effect)
## region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1 entire US 0.802590633 0.0087480764 0.819736862
## 2 pacific 0.003385937 0.0015115719 0.006348618
## 3 east 0.792968005 0.0085672217 0.809759759
## 4 interior west 0.006236691 0.0009201648 0.008040214
## 95 % CI, lower
## 1 0.7854444031
## 2 0.0004232565
## 3 0.7761762504
## 4 0.0044331675A (asymptote of forest biomass in Mg/ha)
## region weighted.A
## 1 entire US 218.8716
## 2 pacific 178.8840
## 3 east 220.3503
## 4 interior west 0.0000K (stand age at half maturation in years)
## region weighted.k
## 1 entire US 69.93156
## 2 pacific 13.16977
## 3 east 70.47598
## 4 interior west 48.58695Model Bookeeping
1. Delta-B due to Delta-STDAGE
2. Delta-B due to Delta-Year (ge)
make a fig
## Warning: Removed 12502 rows containing missing values (`geom_point()`).
3. stand age densities
make a fig
## Warning: package 'ggridges' was built under R version 4.2.2## Picking joint bandwidth of 7.36## Warning: Using the `size` aesthietic with geom_segment was deprecated in ggplot2 3.4.0.
## ℹ Please use the `linewidth` aesthetic instead.
Analysis 2: Temporally-balanced, No-harvest
211 - Northeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3758 873.45
## 2 3726 802.88 32 70.566 10.234 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 40904.91
## 2 2 40336.15##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.76055 0.21445 3.546 0.000395 ***
## alpha 1.18877 0.06983 17.023 < 2e-16 ***
## A 424.79024 35.65526 11.914 < 2e-16 ***
## k 186.51949 17.45686 10.685 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4642 on 3726 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 6.291e-06
## (32 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3726 802.88
## 2 3725 802.88 1 0.00036442 0.0017 0.9672
## model AIC
## 1 2 40336.15
## 2 2a 40338.14
## 3 2b 40332.46
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.72837 0.21189 3.437 0.000594 ***
## alpha 1.19404 0.07036 16.970 < 2e-16 ***
## A 296.71063 41.45441 7.158 9.85e-13 ***
## k 99.70219 21.80438 4.573 4.97e-06 ***
## s 1.17105 0.07830 14.955 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4639 on 3725 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 2.716e-06
## (32 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3756 857.29
## 2 3724 782.82 32 74.47 11.071 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2b 40332.46
## 2 4 40838.67
## 3 5 40245.74##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.94240 0.22839 4.126 3.77e-05 ***
## alpha 1.17324 0.06877 17.060 < 2e-16 ***
## a 37.60901 2.18639 17.201 < 2e-16 ***
## b 107.76147 6.14881 17.526 < 2e-16 ***
## c 115.49056 5.62271 20.540 < 2e-16 ***
## d 0.93145 0.05282 17.634 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4585 on 3724 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (32 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.98688, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -26.722, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
212 - Laurentian Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 10460 3892.5
## 2 7876 2754.4 2584 1138.1 1.2594 1.108e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 109465.57
## 2 2 82497.09##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.33597 0.15467 2.172 0.0299 *
## alpha 0.91328 0.04644 19.664 <2e-16 ***
## A 174.20937 7.60537 22.906 <2e-16 ***
## k 66.00906 3.16091 20.883 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5914 on 7876 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 3.674e-06
## (2590 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7876 2754.4
## 2 7875 2750.2 1 4.214 12.067 0.000516 ***
## 3 7875 2754.4 0 0.000
## 4 7874 2718.8 1 35.554 102.968 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 82497.09
## 2 2a 82487.02
## 3 2b 82498.96
## 4 2c 82398.59##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.41760 0.15914 2.624 0.0087 **
## alpha 0.90560 0.04343 20.850 <2e-16 ***
## A 118.34768 5.85244 20.222 <2e-16 ***
## k 45.43189 1.92530 23.597 <2e-16 ***
## p 0.18195 0.01521 11.962 <2e-16 ***
## s 2.11897 0.15531 13.644 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5876 on 7874 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 8.519e-06
## (2590 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 10458 3839.4
## 2 7874 2711.2 2584 1128.2 1.268 2.114e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2c 82398.59
## 2 4 109325.84
## 3 5 82376.63##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.44439 0.16044 2.77 0.00562 **
## alpha 0.90815 0.04322 21.01 < 2e-16 ***
## a 22.73882 1.25331 18.14 < 2e-16 ***
## b 81.87877 3.62787 22.57 < 2e-16 ***
## c 123.26490 6.80062 18.13 < 2e-16 ***
## d 1.33519 0.06078 21.97 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5868 on 7874 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2590 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
predict and plot
plotting 2
221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4456 722.5
## 2 4422 670.6 34 51.894 10.065 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 48766.23
## 2 2 48164.75##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.5204 0.1598 3.257 0.00113 **
## alpha 0.9229 0.0519 17.783 < 2e-16 ***
## A 444.0211 29.4187 15.093 < 2e-16 ***
## k 143.4409 10.9490 13.101 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3894 on 4422 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 3.693e-06
## (34 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4422 670.60
## 2 4421 669.51 1 1.0958 7.2361 0.007172 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 48164.75
## 2 2a 48159.51
## 3 2b 48142.92
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.57536 0.16350 3.519 0.000437 ***
## alpha 0.93260 0.05238 17.805 < 2e-16 ***
## A 269.98555 21.83371 12.366 < 2e-16 ***
## k 61.89490 6.76412 9.150 < 2e-16 ***
## s 1.33526 0.07232 18.463 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3884 on 4421 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 8.035e-06
## (34 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4454 713.75
## 2 4420 662.39 34 51.355 10.079 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2b 48142.92
## 2 4 48715.91
## 3 5 48114.23##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.60426 0.16462 3.671 0.000245 ***
## alpha 0.92476 0.05168 17.894 < 2e-16 ***
## a 27.90793 3.08437 9.048 < 2e-16 ***
## b 151.78065 8.69980 17.446 < 2e-16 ***
## c 133.03972 10.63119 12.514 < 2e-16 ***
## d 1.31816 0.08221 16.034 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3871 on 4420 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (34 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.98521, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -27.63, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
222 - Midwest Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2793 944.73
## 2 2141 671.57 652 273.16 1.3357 1.3e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## model AIC
## 1 1 30090.45
## 2 2 23141.64##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.01599 0.26220 0.061 0.951
## alpha 0.94372 0.07917 11.921 < 2e-16 ***
## A 532.48363 78.56953 6.777 1.58e-11 ***
## k 233.87556 37.87205 6.175 7.87e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5601 on 2141 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 2.209e-06
## (653 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2141 671.57
## 2 2140 669.22 1 2.3525 7.5226 0.006144 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 23141.64
## 2 2a 23136.12
## 3 2b NA
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.04294 0.26500 0.162 0.871
## alpha 0.96046 0.07927 12.116 < 2e-16 ***
## A 400.61334 62.34054 6.426 1.61e-10 ***
## k 146.96501 32.54757 4.515 6.66e-06 ***
## p -0.02205 0.01203 -1.833 0.067 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5592 on 2140 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 5.035e-06
## (653 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2791 928.22
## 2 2139 655.15 652 273.08 1.3675 1.788e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 23136.12
## 2 4 30045.16
## 3 5 23092.53##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.22531 0.28454 0.792 0.429
## alpha 0.97643 0.07549 12.934 <2e-16 ***
## a 24.12342 2.50787 9.619 <2e-16 ***
## b 119.93339 9.21897 13.009 <2e-16 ***
## c 106.27003 7.30330 14.551 <2e-16 ***
## d 1.04004 0.07193 14.458 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5534 on 2139 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (653 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96143, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -16.089, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
223 - Central Interior Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5108 929.31
## 2 4258 769.03 850 160.28 1.0441 0.204
## model AIC
## 1 1 53477.85
## 2 2 44746.37##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.13289 0.11833 -1.123 0.261
## alpha 0.85046 0.05658 15.031 <2e-16 ***
## A 295.93377 15.87888 18.637 <2e-16 ***
## k 86.90263 6.09681 14.254 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.425 on 4258 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.55e-06
## (850 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4258 769.03
## 2 4257 768.80 1 0.23249 1.2874 0.2566
## model AIC
## 1 2 44746.37
## 2 2a 44747.08
## 3 2b 44714.13
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.10426 0.11946 -0.873 0.383
## alpha 0.86326 0.05695 15.157 <2e-16 ***
## A 191.83961 11.12995 17.236 <2e-16 ***
## k 40.42488 3.02139 13.380 <2e-16 ***
## s 1.48176 0.08512 17.408 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4233 on 4257 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 8.362e-06
## (850 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5106 913.48
## 2 4256 751.00 850 162.49 1.0833 0.06283 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2b 44714.13
## 2 4 53394.02
## 3 5 44649.23##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.08864 0.11921 -0.744 0.457
## alpha 0.85186 0.05587 15.248 <2e-16 ***
## a 29.94864 2.86870 10.440 <2e-16 ***
## b 116.92622 5.31187 22.012 <2e-16 ***
## c 104.05803 5.72271 18.183 <2e-16 ***
## d 1.20947 0.07174 16.859 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4201 on 4256 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (850 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
predict and plot
plotting 2
231 - Southeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6088 1450.4
## 2 5969 1320.6 119 129.79 4.9297 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 66409.03
## 2 2 64981.78##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.49368 0.17211 8.678 <2e-16 ***
## alpha 0.82503 0.04795 17.207 <2e-16 ***
## A 249.29183 10.49290 23.758 <2e-16 ***
## k 65.06575 2.81839 23.086 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4704 on 5969 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 7.397e-06
## (119 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5969 1320.6
## 2 5968 1319.8 1 0.7796 3.525 0.0605 .
## 3 5968 1320.2 0 0.0000
## 4 5967 1308.2 1 11.9851 54.665 1.626e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 64981.78
## 2 2a 64980.25
## 3 2b 64981.97
## 4 2c 64929.50##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.58501 0.17775 8.917 < 2e-16 ***
## alpha 0.83513 0.04688 17.813 < 2e-16 ***
## A 160.41210 8.46170 18.957 < 2e-16 ***
## k 34.73716 1.94017 17.904 < 2e-16 ***
## p 0.09852 0.01425 6.912 5.27e-12 ***
## s 1.69148 0.11557 14.636 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4682 on 5967 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 9.731e-06
## (119 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6086 1437.5
## 2 5967 1307.1 119 130.34 5.0002 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2c 64929.50
## 2 4 66358.45
## 3 5 64924.45##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.56840 0.17681 8.871 <2e-16 ***
## alpha 0.83422 0.04685 17.805 <2e-16 ***
## a 16.88730 1.63137 10.352 <2e-16 ***
## b 127.95506 7.55556 16.935 <2e-16 ***
## c 137.97804 16.47016 8.377 <2e-16 ***
## d 1.78789 0.10347 17.279 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.468 on 5967 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (119 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
predict and plot
plotting 2
232 - Outer Coastal Plain Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6290 2432.4
## 2 6150 2239.5 140 192.94 3.7845 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 70632.57
## 2 2 69030.05##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.05946 0.19441 5.45 5.24e-08 ***
## alpha 0.78664 0.04693 16.76 < 2e-16 ***
## A 258.22071 13.82230 18.68 < 2e-16 ***
## k 69.01364 3.82624 18.04 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6034 on 6150 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.681e-06
## (142 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6150 2239.5
## 2 6149 2233.3 1 6.1935 17.052 3.684e-05 ***
## 3 6149 2239.3 0 0.0000
## 4 6148 2213.4 1 25.8828 71.891 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 69030.05
## 2 2a 69015.01
## 3 2b 69031.60
## 4 2c 68962.05##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.19119 0.20278 5.874 4.47e-09 ***
## alpha 0.81085 0.04401 18.425 < 2e-16 ***
## A 158.53548 9.39510 16.874 < 2e-16 ***
## k 36.29188 2.12763 17.057 < 2e-16 ***
## p 0.12742 0.01578 8.075 8.06e-16 ***
## s 1.87087 0.14548 12.860 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6 on 6148 degrees of freedom
##
## Number of iterations to convergence: 17
## Achieved convergence tolerance: 5.625e-06
## (142 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6288 2414.5
## 2 6148 2212.5 140 202.02 4.0099 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2c 68962.05
## 2 4 70589.95
## 3 5 68959.28##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.17160 0.20149 5.815 6.38e-09 ***
## alpha 0.80939 0.04399 18.399 < 2e-16 ***
## a 20.89438 1.77891 11.746 < 2e-16 ***
## b 127.00119 8.66265 14.661 < 2e-16 ***
## c 137.92562 17.86323 7.721 1.34e-14 ***
## d 1.67730 0.11014 15.229 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5999 on 6148 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (142 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
predict and plot
plotting 2
234 - Lower Mississippi Riverine Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 675 158.75
## 2 653 137.82 22 20.932 4.5079 7.916e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 7483.277
## 2 2 7228.714##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.5365 0.4799 1.118 0.264026
## alpha 0.8974 0.1033 8.688 < 2e-16 ***
## A 578.9666 141.8010 4.083 5e-05 ***
## k 194.2614 54.2443 3.581 0.000367 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4594 on 653 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.838e-06
## (27 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_234, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 653 137.82
## 2 652 137.77 1 0.053795 0.2546 0.614
## model AIC
## 1 2 7228.714
## 2 2a 7230.457
## 3 2b 7230.618
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.5365 0.4799 1.118 0.264026
## alpha 0.8974 0.1033 8.688 < 2e-16 ***
## A 578.9666 141.8010 4.083 5e-05 ***
## k 194.2614 54.2443 3.581 0.000367 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4594 on 653 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.838e-06
## (27 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Error in nls(f_5, data = G_234, start = c(tau = tau.start, alpha = alpha.start, :
## Convergence failure: iteration limit reached without convergence (10)
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 673 158.11
## 2 795 176.77 -122 -18.654 0.6508 0.9981
## model AIC
## 1 2 7228.714
## 2 4 7484.532
## 3 5 8723.743##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.5365 0.4799 1.118 0.264026
## alpha 0.8974 0.1033 8.688 < 2e-16 ***
## A 578.9666 141.8010 4.083 5e-05 ***
## k 194.2614 54.2443 3.581 0.000367 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4594 on 653 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.838e-06
## (27 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96055, p-value = 2.77e-12
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -9.2684, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
242 - Pacific Lowland Mixed Forest
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"251 - Prairie Parkland (Temperate)
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1213 319.61
## 2 866 178.11 347 141.49 1.9826 9.693e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 12758.145
## 2 2 9001.833##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.5936 0.4321 1.374 0.17
## alpha 0.7574 0.1119 6.767 2.42e-11 ***
## A 240.5767 34.4469 6.984 5.72e-12 ***
## k 99.7638 16.3415 6.105 1.55e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4535 on 866 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 2.039e-06
## (348 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 866 178.11
## 2 865 177.69 1 0.42531 2.0705 0.1505
## model AIC
## 1 2 9001.833
## 2 2a 9001.753
## 3 2b 8998.361
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.5812 0.4286 1.356 0.175
## alpha 0.7736 0.1123 6.891 1.07e-11 ***
## A 153.3669 24.2442 6.326 4.03e-10 ***
## k 44.7379 8.6216 5.189 2.64e-07 ***
## s 1.4762 0.2154 6.854 1.36e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4524 on 865 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 2.869e-06
## (348 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1211 309.99
## 2 864 175.99 347 134 1.8957 6.464e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2b 8998.361
## 2 4 12724.990
## 3 5 8995.414##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.5935 0.4294 1.382 0.16727
## alpha 0.7684 0.1126 6.824 1.67e-11 ***
## a 24.4359 7.1577 3.414 0.00067 ***
## b 91.9391 13.0777 7.030 4.19e-12 ***
## c 114.3717 17.3683 6.585 7.89e-11 ***
## d 1.2279 0.1998 6.146 1.21e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4513 on 864 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (348 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.97063, p-value = 3.094e-12
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -8.1225, p-value = 4.569e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
255 - Prairie Parkland (Subtropical)
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 408 218.09
## 2 384 184.75 24 33.343 2.8877 1.026e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 4302.110
## 2 2 4087.713##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.4395 0.4776 -0.920 0.358043
## alpha 0.5924 0.1622 3.652 0.000297 ***
## A 191.8035 37.3817 5.131 4.59e-07 ***
## k 52.7150 12.4724 4.227 2.97e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6936 on 384 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.496e-06
## (24 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 384 184.75
## 2 383 181.12 1 3.6224 7.6598 0.00592 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 4087.713
## 2 2a 4082.029
## 3 2b 4087.527
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.35911 0.49401 -0.727 0.467710
## alpha 0.58110 0.14985 3.878 0.000124 ***
## A 289.31044 134.85478 2.145 0.032553 *
## k 128.69919 90.87880 1.416 0.157541
## p 0.04193 0.01342 3.124 0.001922 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6877 on 383 degrees of freedom
##
## Number of iterations to convergence: 17
## Achieved convergence tolerance: 6.545e-06
## (24 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 406 207.53
## 2 382 171.16 24 36.375 3.3827 2.915e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2a 4082.029
## 2 4 4285.720
## 3 5 4062.072##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.3922 0.4717 -0.831 0.406
## alpha 0.6720 0.1409 4.768 2.65e-06 ***
## a 24.3766 3.5771 6.815 3.69e-11 ***
## b 78.2871 10.8889 7.190 3.45e-12 ***
## c 56.0643 6.1528 9.112 < 2e-16 ***
## d 0.9506 0.1362 6.979 1.32e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6694 on 382 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (24 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93842, p-value = 1.363e-11
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.4913, p-value = 7.078e-06
## alternative hypothesis: two.sidedpredict and plot
plotting 2
261 - California Coastal Chaparral Forest and Shrub
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
add p model: does not fit
add s model: does not fit
add s+p model: does not fit
unable to fit model (only 64 observations)
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"262 - California Dry Steppe
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
add p model: does not fit
add s model: does not fit
add s+p model: does not fit
unable to fit model (0 observations)
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"263 - California Coastal Steppe - Mixed Forest and Redwood Forest
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"313 - Colorado Plateau Semi-Desert
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"315 - Southwest Plateau and Plains Dry Steppe and Shrub
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"321 - Chihuahuan Semi-Desert
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"322 - American Semidesert and Desert
model selection 1
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed## model AIC
## 1 1 NA
## 2 2 NA## Warning in min(AIC1_322$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_322.' not foundsummary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"- Cannot fit model
- not enough data (only 3 observations)
331 - Great Plains/Palouse Dry Steppe
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"- Cannot fit model
332 - Great Plains Steppe
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 141 88.067
## 2 127 75.692 14 12.375 1.4831 0.1264
## model AIC
## 1 1 1555.082
## 2 2 1422.430##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.106 2.299 0.481 0.631
## alpha 1.043 0.232 4.494 1.55e-05 ***
## A 167.129 102.643 1.628 0.106
## k 86.630 58.626 1.478 0.142
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.772 on 127 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.906e-06
## (15 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_332, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_332, :
## number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 2 1422.43
## 2 2a NA
## 3 2b NA
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.106 2.299 0.481 0.631
## alpha 1.043 0.232 4.494 1.55e-05 ***
## A 167.129 102.643 1.628 0.106
## k 86.630 58.626 1.478 0.142
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.772 on 127 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.906e-06
## (15 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 139 82.744
## 2 125 69.806 14 12.938 1.6548 0.07363 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 1422.430
## 2 4 1550.105
## 3 5 1415.826##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.5672 2.6040 0.602 0.5484
## alpha 1.0506 0.2270 4.627 9.14e-06 ***
## a 26.2968 14.3835 1.828 0.0699 .
## b 49.0289 25.3233 1.936 0.0551 .
## c 90.3751 38.5828 2.342 0.0207 *
## d 0.9109 0.4962 1.836 0.0688 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7473 on 125 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (15 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.87384, p-value = 3.588e-09
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -3.501, p-value = 0.0004635
## alternative hypothesis: two.sidedpredict and plot
plotting 2
341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"- model not fitted because only 62 observations
predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"342 - Intermountain Semi-Desert
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"411 - Everglades
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3966 645.80
## 2 3952 609.53 14 36.262 16.793 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 42166.19
## 2 2 41840.90##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.07467 0.21865 4.915 9.24e-07 ***
## alpha 0.90960 0.06581 13.822 < 2e-16 ***
## A 386.41867 27.73826 13.931 < 2e-16 ***
## k 178.58145 13.13977 13.591 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3927 on 3952 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.553e-06
## (14 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3952 609.53
## 2 3951 605.64 1 3.8897 25.375 4.931e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 41840.90
## 2 2a 41817.58
## 3 2b 41800.23
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.92749 0.20677 4.486 7.47e-06 ***
## alpha 0.93841 0.06619 14.177 < 2e-16 ***
## A 217.97071 15.91105 13.699 < 2e-16 ***
## k 64.33797 6.20942 10.361 < 2e-16 ***
## s 1.38818 0.06640 20.907 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3907 on 3951 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 3.78e-06
## (14 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3964 637.04
## 2 3950 600.06 14 36.985 17.39 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2b 41800.23
## 2 4 42116.02
## 3 5 41782.90##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.00143 0.21329 4.695 2.75e-06 ***
## alpha 0.94619 0.06507 14.542 < 2e-16 ***
## a 21.16601 2.88388 7.339 2.59e-13 ***
## b 131.27072 8.83261 14.862 < 2e-16 ***
## c 156.42672 14.16203 11.046 < 2e-16 ***
## d 1.39288 0.09318 14.949 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3898 on 3950 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (14 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.98839, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -26.733, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4620 758.87
## 2 4593 719.43 27 39.437 9.3248 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 51198.35
## 2 2 50731.36##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.78480 0.14404 5.449 5.34e-08 ***
## alpha 0.91764 0.06205 14.789 < 2e-16 ***
## A 258.54261 10.28744 25.132 < 2e-16 ***
## k 59.04328 3.19504 18.480 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3958 on 4593 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.825e-06
## (27 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4593 719.43
## 2 4592 718.57 1 0.8579 5.4825 0.01925 *
## 3 4592 714.19 0 0.0000
## 4 4591 703.14 1 11.0492 72.1436 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 50731.36
## 2 2a 50727.88
## 3 2b 50699.74
## 4 2c 50630.06##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.95521 0.15274 6.254 4.37e-10 ***
## alpha 0.92578 0.06043 15.321 < 2e-16 ***
## A 159.86389 5.76420 27.734 < 2e-16 ***
## k 38.48498 1.13710 33.845 < 2e-16 ***
## p 0.24420 0.02081 11.736 < 2e-16 ***
## s 2.88617 0.24010 12.021 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3914 on 4591 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 3.107e-06
## (27 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4618 743.42
## 2 4591 702.06 27 41.361 10.018 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2c 50630.06
## 2 4 51107.25
## 3 5 50622.97##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.94893 0.15197 6.244 4.65e-10 ***
## alpha 0.92236 0.06059 15.223 < 2e-16 ***
## a 37.86675 3.02947 12.499 < 2e-16 ***
## b 115.58994 4.82746 23.944 < 2e-16 ***
## c 101.67398 3.95996 25.676 < 2e-16 ***
## d 1.19560 0.06247 19.140 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3911 on 4591 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (27 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96838, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -26.709, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M223 - Ozark Broadleaf Forest Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 523 64.694
## 2 521 60.692 2 4.0019 17.177 5.969e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 5359.324
## 2 2 5320.473##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.03335 0.28391 -0.117 0.907
## alpha 0.95993 0.15629 6.142 1.62e-09 ***
## A 308.68739 47.34757 6.520 1.67e-10 ***
## k 100.73887 21.37371 4.713 3.13e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3413 on 521 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 9.364e-07
## (3 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M223, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 521 60.692
## 2 520 60.589 1 0.10356 0.8888 0.3462
## model AIC
## 1 2 5320.473
## 2 2a 5321.577
## 3 2b 5321.974
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.03335 0.28391 -0.117 0.907
## alpha 0.95993 0.15629 6.142 1.62e-09 ***
## A 308.68739 47.34757 6.520 1.67e-10 ***
## k 100.73887 21.37371 4.713 3.13e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3413 on 521 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 9.364e-07
## (3 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 521 64.501
## 2 519 60.606 2 3.8948 16.677 9.565e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 5320.473
## 2 4 5361.749
## 3 5 5323.726##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.03335 0.28391 -0.117 0.907
## alpha 0.95993 0.15629 6.142 1.62e-09 ***
## A 308.68739 47.34757 6.520 1.67e-10 ***
## k 100.73887 21.37371 4.713 3.13e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3413 on 521 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 9.364e-07
## (3 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96244, p-value = 2.54e-10
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -8.9577, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M231 - Ouachita Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 586 115.11
## 2 583 110.96 3 4.1518 7.2716 8.551e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 6079.429
## 2 2 6046.192##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.4484 0.4959 0.904 0.366192
## alpha 0.8699 0.2292 3.795 0.000163 ***
## A 485.7390 149.6379 3.246 0.001237 **
## k 255.8678 86.8725 2.945 0.003355 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4363 on 583 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 2.808e-06
## (3 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 583 110.96
## 2 582 110.64 1 0.31117 1.6368 0.2013
## model AIC
## 1 2 6046.192
## 2 2a 6046.543
## 3 2b 6914.673
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.4484 0.4959 0.904 0.366192
## alpha 0.8699 0.2292 3.795 0.000163 ***
## A 485.7390 149.6379 3.246 0.001237 **
## k 255.8678 86.8725 2.945 0.003355 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4363 on 583 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 2.808e-06
## (3 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 584 114.44
## 2 581 110.29 3 4.1455 7.2793 8.464e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 6046.192
## 2 4 6079.986
## 3 5 6046.664##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.4484 0.4959 0.904 0.366192
## alpha 0.8699 0.2292 3.795 0.000163 ***
## A 485.7390 149.6379 3.246 0.001237 **
## k 255.8678 86.8725 2.945 0.003355 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4363 on 583 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 2.808e-06
## (3 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96265, p-value = 4.65e-11
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -9.4958, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M242 - Cascade Mixed Forest
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 308 94.545
## 2 150 49.447 158 45.098 0.8659 0.8142
## model AIC
## 1 1 3309.570
## 2 2 1656.873##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.4572 1.4782 -0.986 0.3258
## alpha 0.7454 0.2859 2.607 0.0101 *
## A 189.4205 134.0559 1.413 0.1597
## k 12.1167 10.5064 1.153 0.2506
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5741 on 150 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 6.427e-06
## (158 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 150 49.447
## 2 149 49.248 1 0.19855 0.6007 0.4395
## model AIC
## 1 2 1656.873
## 2 2a 1658.254
## 3 2b NA
## 4 2c NA##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.4572 1.4782 -0.986 0.3258
## alpha 0.7454 0.2859 2.607 0.0101 *
## A 189.4205 134.0559 1.413 0.1597
## k 12.1167 10.5064 1.153 0.2506
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5741 on 150 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 6.427e-06
## (158 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 306 91.857
## 2 148 47.700 158 44.157 0.8671 0.8111
## model AIC
## 1 2 1656.873
## 2 4 3304.600
## 3 5 1655.335##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.5315 1.3560 -1.129 0.261
## alpha 0.6259 0.3236 1.934 0.055 .
## a 0.0000 186.8284 0.000 1.000
## b 186.0902 217.3750 0.856 0.393
## c 116.1885 19.5549 5.942 1.94e-08 ***
## d 1.8167 1.2953 1.402 0.163
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5677 on 148 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (158 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.981, p-value = 0.03198
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = 1.0065, p-value = 0.3142
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M262 - California coastal range - coniferous forest - open woodland - shrub meadow
Model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"- model can fit - but K is negative (only 19 observations) - model excluded
predict and plot
## [1] "cannot plot data with prediction"plotting 2
M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M334 - Black Hills Coniferous Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 247 102.69
## 2 176 77.97 71 24.724 0.786 0.8767
## model AIC
## 1 1 2514.590
## 2 2 1827.743##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.4470 0.9878 -0.453 0.65143
## alpha 0.7713 0.2129 3.623 0.00038 ***
## A 113.8241 36.5520 3.114 0.00215 **
## k 50.8899 25.0112 2.035 0.04338 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6656 on 176 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 6.267e-06
## (74 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_M334, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M334, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 176 77.970
## 2 212 86.587 -36 -8.6171 0.5403 0.9845
## 3 175 77.471 37 9.1156 0.5565 0.9814
## 4 211 86.173 -36 -8.7017 0.5460 0.9830
## model AIC
## 1 2 1827.743
## 2 2a 2168.486
## 3 2b 1828.588
## 4 2c 2169.446##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.4470 0.9878 -0.453 0.65143
## alpha 0.7713 0.2129 3.623 0.00038 ***
## A 113.8241 36.5520 3.114 0.00215 **
## k 50.8899 25.0112 2.035 0.04338 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6656 on 176 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 6.267e-06
## (74 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
model selection 3
## Analysis of Variance Table
##
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 245 102.324
## 2 174 77.733 71 24.59 0.7753 0.8895
## model AIC
## 1 2 1827.743
## 2 4 2517.688
## 3 5 1831.196##
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha *
## B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.4470 0.9878 -0.453 0.65143
## alpha 0.7713 0.2129 3.623 0.00038 ***
## A 113.8241 36.5520 3.114 0.00215 **
## k 50.8899 25.0112 2.035 0.04338 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6656 on 176 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 6.267e-06
## (74 observations deleted due to missingness)summary
- simple log-normal model: fits
- log-normal phi model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93019, p-value = 1.28e-07
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -3.836, p-value = 0.0001251
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
model selection 3
summary
- simple log-normal model: does not fit
- log-normal phi model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
Fitted parameters
Best / selected models by ecoprovince
| Code | Ecoregion | Sel.Mod.2 | Sel.Mod.3 | Best.Mod |
|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | 2b | 5 | 5 |
| 212 | Laurentian Mixed Forest | 2c | 5 | 5 |
| 221 | Eastern Broadleaf Forest | 2b | 5 | 5 |
| 222 | Midwest Broadleaf Forest | 2a | 5 | 5 |
| 223 | Central Interior Broadleaf Forest | 2b | 5 | 5 |
| 231 | Southeastern Mixed Forest | 2c | 5 | 5 |
| 232 | Outer Coastal Plain Mixed Forest | 2c | 5 | 5 |
| 234 | Lower Mississippi Riverine Forest | 2 | 2 | 2 |
| 242 | Pacific Lowland Mixed Forest | NA | NA | NA |
| 251 | Prairie Parkland (Temperate) | 2b | 5 | 5 |
| 255 | Prairie Parkland (Subtropical) | 2a | 5 | 5 |
| 261 | California Coastal Chaparral Forest and Shrub | NA | NA | NA |
| 262 | California Dry Steppe | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | NA | NA | NA |
| 313 | Colorado Plateau Semi-Desert | NA | NA | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | NA | NA | NA |
| 322 | American Semidesert and Desert | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | NA | NA | NA |
| 332 | Great Plains Steppe | 2 | 5 | 5 |
| 341 | Intermountain Semi-Desert and Desert | NA | NA | NA |
| 342 | Intermountain Semi-Desert | NA | NA | NA |
| 411 | Everglades | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | 2b | 5 | 5 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | 2c | 5 | 5 |
| M223 | Ozark Broadleaf Forest Meadow | 2 | 2 | 2 |
| M231 | Ouachita Mixed Forest | 2 | 2 | 2 |
| M242 | Cascade Mixed Forest | NA | NA | NA |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | 2 | 5 | 5 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | NA | NA | NA |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | NA | NA | NA |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | NA | NA | NA |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | NA | NA | NA |
| M334 | Black Hills Coniferous Forest | 2 | 2 | 2 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | NA | NA | NA |
table by ecoprovince
| Code | Ecoregion | region | n.obs | n.plots | tau | tau.variance | tau.2.5 | tau.97.5 | alpha | alpha.variance | alpha.2.5 | alpha.97.5 | A | A.2.5 | A.97.5 | k | k.2.5 | k.97.5 | a | a.2.5 | a.97.5 | b | b.se | b.2.5 | b.97.5 | c | c.2.5 | c.97.5 | d | d.2.5 | d.97.5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | east | 4838 | 2419 | 0.9424031 | 0.0521622 | 0.4946206 | 1.3901857 | 1.1732355 | 0.0047294 | 1.0384042 | 1.3080667 | 296.7106 | 215.43507 | 377.9862 | 99.70219 | 56.952511 | 142.45188 | 37.60901 | 33.322363 | 41.89566 | 107.76147 | NA | 95.706112 | 119.81683 | 115.49056 | 104.46666 | 126.51445 | 0.9314542 | 0.8278945 | 1.035014 |
| 212 | Laurentian Mixed Forest | east | 12962 | 6481 | 0.4443891 | 0.0257410 | 0.1298840 | 0.7588942 | 0.9081521 | 0.0018684 | 0.8234201 | 0.9928841 | 118.3477 | 106.87534 | 129.8200 | 45.43189 | 41.657800 | 49.20598 | 22.73882 | 20.282002 | 25.19564 | 81.87877 | NA | 74.767183 | 88.99036 | 123.26490 | 109.93388 | 136.59592 | 1.3351866 | 1.2160475 | 1.454326 |
| 221 | Eastern Broadleaf Forest | east | 5446 | 2723 | 0.6042576 | 0.0270982 | 0.2815289 | 0.9269862 | 0.9247619 | 0.0026709 | 0.8234423 | 1.0260816 | 269.9856 | 227.18055 | 312.7906 | 61.89490 | 48.633836 | 75.15597 | 27.90793 | 21.861033 | 33.95484 | 151.78065 | NA | 134.724680 | 168.83662 | 133.03972 | 112.19726 | 153.88218 | 1.3181638 | 1.1569938 | 1.479334 |
| 222 | Midwest Broadleaf Forest | east | 3552 | 1776 | 0.2253071 | 0.0809640 | -0.3327003 | 0.7833144 | 0.9764315 | 0.0056993 | 0.8283833 | 1.1244797 | 400.6133 | 278.35898 | 522.8677 | 146.96501 | 83.136845 | 210.79317 | 24.12342 | 19.205295 | 29.04154 | 119.93339 | NA | 101.854303 | 138.01247 | 106.27003 | 91.94773 | 120.59233 | 1.0400449 | 0.8989773 | 1.181113 |
| 223 | Central Interior Broadleaf Forest | east | 6388 | 3194 | -0.0886365 | 0.0142121 | -0.3223588 | 0.1450858 | 0.8518610 | 0.0031213 | 0.7423297 | 0.9613923 | 191.8396 | 170.01911 | 213.6601 | 40.42488 | 34.501375 | 46.34838 | 29.94864 | 24.324500 | 35.57278 | 116.92622 | NA | 106.512186 | 127.34025 | 104.05803 | 92.83853 | 115.27754 | 1.2094657 | 1.0688136 | 1.350118 |
| 231 | Southeastern Mixed Forest | east | 7790 | 3895 | 1.5683967 | 0.0312611 | 1.2217888 | 1.9150045 | 0.8342248 | 0.0021951 | 0.7423777 | 0.9260719 | 160.4121 | 143.82410 | 177.0001 | 34.73716 | 30.933723 | 38.54059 | 16.88730 | 13.689232 | 20.08536 | 127.95506 | NA | 113.143429 | 142.76670 | 137.97804 | 105.69057 | 170.26552 | 1.7878861 | 1.5850468 | 1.990725 |
| 232 | Outer Coastal Plain Mixed Forest | east | 7940 | 3970 | 1.1715993 | 0.0405997 | 0.7766012 | 1.5665975 | 0.8093879 | 0.0019352 | 0.7231514 | 0.8956244 | 158.5355 | 140.11780 | 176.9532 | 36.29188 | 32.120973 | 40.46279 | 20.89438 | 17.407091 | 24.38167 | 127.00119 | NA | 110.019361 | 143.98302 | 137.92562 | 102.90745 | 172.94379 | 1.6773002 | 1.4613897 | 1.893211 |
| 234 | Lower Mississippi Riverine Forest | east | 830 | 415 | 0.5365186 | 0.2303423 | -0.4058930 | 1.4789303 | 0.8974205 | 0.0106700 | 0.6945892 | 1.1002519 | 578.9666 | 300.52578 | 857.4075 | 194.26139 | 87.747074 | 300.77571 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 242 | Pacific Lowland Mixed Forest | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 251 | Prairie Parkland (Temperate) | east | 1392 | 696 | 0.5935494 | 0.1844038 | -0.2492842 | 1.4363829 | 0.7683810 | 0.0126797 | 0.5473712 | 0.9893908 | 153.3669 | 105.78254 | 200.9513 | 44.73786 | 27.816115 | 61.65961 | 24.43590 | 10.387458 | 38.48434 | 91.93913 | NA | 66.271403 | 117.60686 | 114.37173 | 80.28268 | 148.46079 | 1.2279283 | 0.8357726 | 1.620084 |
| 255 | Prairie Parkland (Subtropical) | east | 444 | 222 | -0.3921830 | 0.2224859 | -1.3196054 | 0.5352393 | 0.6719845 | 0.0198603 | 0.3948956 | 0.9490735 | 289.3104 | 24.16204 | 554.4588 | 128.69919 | -49.984634 | 307.38301 | 24.37657 | 17.343350 | 31.40978 | 78.28708 | NA | 56.877418 | 99.69675 | 56.06428 | 43.96678 | 68.16178 | 0.9505970 | 0.6827878 | 1.218406 |
| 261 | California Coastal Chaparral Forest and Shrub | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 262 | California Dry Steppe | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | pacific | 4 | 2 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 313 | Colorado Plateau Semi-Desert | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 322 | American Semidesert and Desert | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | interior west | 118 | 59 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 332 | Great Plains Steppe | interior west | 154 | 77 | 1.5671503 | 6.7810091 | -3.5865623 | 6.7208629 | 1.0505657 | 0.0515516 | 0.6012062 | 1.4999252 | 167.1286 | -35.98320 | 370.2403 | 86.63024 | -29.379580 | 202.64005 | 26.29682 | -2.169919 | 54.76357 | 49.02886 | NA | -1.089147 | 99.14686 | 90.37508 | 14.01489 | 166.73527 | 0.9108652 | -0.0711632 | 1.892894 |
| 341 | Intermountain Semi-Desert and Desert | interior west | 4 | 2 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 342 | Intermountain Semi-Desert | interior west | 2 | 1 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 411 | Everglades | east | 66 | 33 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | east | 5108 | 2554 | 1.0014343 | 0.0454934 | 0.5832618 | 1.4196067 | 0.9461881 | 0.0042335 | 0.8186231 | 1.0737531 | 217.9707 | 186.77606 | 249.1654 | 64.33797 | 52.163996 | 76.51195 | 21.16601 | 15.511965 | 26.82005 | 131.27072 | NA | 113.953817 | 148.58763 | 156.42672 | 128.66114 | 184.19229 | 1.3928757 | 1.2101952 | 1.575556 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | east | 5186 | 2593 | 0.9489282 | 0.0230962 | 0.6509857 | 1.2468707 | 0.9223633 | 0.0036710 | 0.8035806 | 1.0411460 | 159.8639 | 148.56328 | 171.1645 | 38.48498 | 36.255709 | 40.71424 | 37.86675 | 31.927529 | 43.80597 | 115.58994 | NA | 106.125791 | 125.05408 | 101.67398 | 93.91056 | 109.43740 | 1.1955984 | 1.0731328 | 1.318064 |
| M223 | Ozark Broadleaf Forest Meadow | east | 602 | 301 | -0.0333485 | 0.0806076 | -0.5911068 | 0.5244099 | 0.9599312 | 0.0244255 | 0.6529016 | 1.2669608 | 308.6874 | 215.67178 | 401.7030 | 100.73887 | 58.749635 | 142.72811 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M231 | Ouachita Mixed Forest | east | 680 | 340 | 0.4484485 | 0.2459056 | -0.5254974 | 1.4223945 | 0.8699411 | 0.0525445 | 0.4197321 | 1.3201501 | 485.7390 | 191.84391 | 779.6341 | 255.86783 | 85.246686 | 426.48898 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M242 | Cascade Mixed Forest | pacific | 34 | 17 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | pacific | 330 | 165 | -1.5315111 | 1.8388175 | -4.2111926 | 1.1481704 | 0.6259333 | 0.1047002 | -0.0134886 | 1.2653553 | 189.4205 | -75.46132 | 454.3022 | 12.11667 | -8.643067 | 32.87642 | 0.00000 | -369.195820 | 369.19582 | 186.09019 | NA | -243.469483 | 615.64987 | 116.18850 | 77.54570 | 154.83130 | 1.8166738 | -0.7430680 | 4.376416 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | interior west | 8 | 4 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 20 | 10 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 22 | 11 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M334 | Black Hills Coniferous Forest | interior west | 306 | 153 | -0.4470264 | 0.9757402 | -2.3964750 | 1.5024223 | 0.7712933 | 0.0453143 | 0.3511838 | 1.1914028 | 113.8241 | 41.68754 | 185.9606 | 50.88991 | 1.529410 | 100.25040 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | interior west | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
plot tau
map
## OGR data source with driver: ESRI Shapefile
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings: PROVINCE_ PROVINCE_I
plot alpha (biomass compensation effect)
plot A (asymptote of B)
## Warning: Removed 19 rows containing missing values (`geom_point()`).
plot k (stand age at half biomass asymptote)
## Warning: Removed 19 rows containing missing values (`geom_point()`).
Caclulations - weighted averages
ge (stand biomass enhancement factor in % 2000-2021)
## region weighted.tau weighted.tau.std_Error 95 % CI, upper
## 1 entire US 0.722177703 0.061043361 0.841822689
## 2 pacific -0.007869066 0.006967426 0.005787089
## 3 east 0.728418907 0.060138268 0.846289912
## 4 interior west 0.001627862 0.007818922 0.016952949
## 95 % CI, lower
## 1 0.60253272
## 2 -0.02152522
## 3 0.61054790
## 4 -0.01369722alpha (biomass compensation effect)
## region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1 entire US 0.900290679 5.428050e-07 0.900291743
## 2 pacific 0.003216112 5.177211e-08 0.003216213
## 3 east 0.890880769 5.391401e-07 0.890881825
## 4 interior west 0.006193798 3.584505e-08 0.006193868
## 95 % CI, lower
## 1 0.900289615
## 2 0.003216010
## 3 0.890879712
## 4 0.006193728A (asymptote of forest biomass in Mg/ha)
## region weighted.A
## 1 entire US 202.4230
## 2 pacific 169.8607
## 3 east 203.6845
## 4 interior west 0.0000K (stand age at half maturation in years)
## region weighted.k
## 1 entire US 59.53607
## 2 pacific 10.86550
## 3 east 59.95906
## 4 interior west 45.60468Model Bookeeping
1. Delta-B due to Delta-STDAGE
2. Delta-B due to Delta-Year (ge)
make a fig
## Warning: Removed 10136 rows containing missing values (`geom_point()`).
3. stand age densities
make a fig
## Picking joint bandwidth of 7.36
